Rolling stand for producing rolled strip

ABSTRACT

In the case of a rolling stand for producing rolled strip, which is provided with rolls which are axially displaceable with respect to one another, have a curved contour running over the entire effective barrel length and complement one another exclusively in a specific relative axial position of the rolls in the unloaded state, it is intended for the thickness profile of the roll gap over the active roll barrel length to be varied by axial displacement of the rolls provided with a roll barrel contour in relation to one another in such a way that a strip that is planar and free from undulations is obtained. This takes place by the profile of the barrel contour of the rolls of a pair of rolls being formed by a trigonometric function and the roll gap contour also being formed by a trigonometric function in dependence on the profile of the barrel contour and the position of the rolls within the axial displacement region.

BACKGROUND OF THE INVENTION

The invention relates to a rolling stand for producing rolled strip,with work rolls which are supported if appropriate on backup rolls orbackup rolls and intermediate rolls. The work rolls and/or backup rollsand/or intermediate rolls are arranged such that they are axiallydisplaceable with respect to one another in the rolling stand. Each rollof at least one of these pairs of rolls has curved contour running overthe entire effective barrel length. These two barrel contoursexclusively complement one another at a specific axial position of therolls of the pair of rolls with respect to each other and in theunloaded state.

To produce a planar rolled strip with a defined cross-sectional profile,it is necessary to set contour-influencing measures, such as for examplethe use of roll bending devices, with which the application of rollingforce to the strip and the distribution of the exiting thickness overthe width of the strip can be influenced in a specifically selectivemanner.

EP-B 0 049 798 already discloses a rolling stand of the generic type inwhich the form of the roll gap, and consequently the surface contour ofthe rolled strip, is influenced exclusively by the axial displacement ofthe rolls formed with curved contours. The two interacting rolls of apair of rolls have an identical form, are installed in 180° oppositionand complement one another in a specific axial displacement position.This particular camber of the rolls makes it possible to compensate forthe parabolic roll barrel bending under load, which is dependent on therespective loading conditions, so that a roll change necessary whenthere is a significant change in the loading conditions, which is quitecustomary in the case of rolls with a parabolic roll barrel camber, isno longer needed. In EP-B 294 544 it is pointed out that the parabolicbending determined essentially by quadratic components can becompensated by axially displaceable rolls with the described rollcontour, but excessive stretching in the edge areas or in the quarterareas of the rolled strip can lead to undulations in the edge or quarterarea. Although these disadvantages could be overcome with additionalroll bending devices, expediently in combination with zone cooling,major advantages of rolls contoured in such a way would be lost again asa result.

According to EP-B 294 544, to avoid this formation of undulations at theedge or quarter area on the rolled strip, it is proposed that the rollbarrel contours of the rolls complementing one other in an axialdisplacement position are formed by a curve of the fifth order, therespective curves being placed on the rolls in such a way that, in aneutral roll position, they have a maximum and minimum of theinclination of the curves respectively in linear regions situated oneither side of the center.

SUMMARY OF THE INVENTION

The object of the present invention is to provide a further advantageoussolution for a rolling stand in which the form of the roll gap, i.e. thethickness profile of the roll gap over the active roll barrel length,can be varied by axial displacement of the rolls provided with a rollbarrel contour in relation to one another in such a way that a stripwhich meets the highest quality requirements, is planar and free fromundulations is obtained.

This object is achieved according to the invention by the profile of thebarrel contour of the rolls of a pair of rolls being formed by atrigonometric function and the roll gap contour also being formed by atrigonometric function in dependence on the profile of the barrelcontour and the position of the rolls within the axial displacementregion.

Tests have shown that good results can be obtained if the trigonometricfunction of the barrel contour is formed by a sine function and the rollgap contour is formed by a cosine function derived from said sinefunction. The barrel contour in this case follows the general equation

${R(x)} = {R_{0} + {A*{\sin\left( \frac{2*\varphi*\left( {x + c} \right)}{L_{REF}} \right)}}}$where

-   R is the radius of the roll-   x is the axial position with respect to the center of the roll    (=distance from the center of the roll)-   R₀ is the roll radius offset (=radius of the roll at the contour    inflection point)-   A is the contour coefficient-   φ is the contour angle-   c is the contour displacement-   L_(REF) is the camber reference length

The roll gap contour in this case follows the general equation

${G\left( {x,s} \right)} = {G_{0} + {2*A*{\cos\left( \frac{2*\varphi*x}{L_{REF}} \right)}*{\sin\left( \frac{2*\varphi*\left( {s - c} \right)}{L_{REF}} \right)}}}$where

-   s is the displacement of the upper roll from the central position-   G₀ is the roll gap offset    and is obtained from the contour equations of the two roll barrels    with the inclusion of the displacement distance (s) of one of the    rolls from the central position.

The contour coefficient A is in this case determined by the axialdisplacement region and the corresponding equivalent roll cambers in theextreme positions of the rolls. Equivalent camber is understood in thiscase as meaning that camber of conventional rolls provided with a cosinecamber which together generate exactly the same idle roll gap profile.

By varying the contour angle φ, which relates to half the camberreference length, the current roll contour, and consequently the profileof the roll gap, can be influenced without changing the equivalentcambers of the rolls. The positive effect with regard to avoidance ofthe formation of undulations in the quarter area is obtained, because anincrease in the contour angle leads to a decrease in the roll barreldiameter in the region between the edge of the roll and the center ofthe roll, whereby ultimately a smaller rolling deformation occurs inthis region that is critical for the formation of undulations in thequarter area.

A particularly advantageous configuration of a rolling stand is obtainedif the trigonometric function of the barrel contour is formed by atilted sine function corresponding to the general equation

${R(x)} = {R_{0} + {A*{\sin\left( \frac{2*\varphi*\left( {x + c} \right)}{L_{REF}} \right)}} + {B*\left( {x + c} \right)}}$where

-   B is the tilting coefficient    and the roll gap contour is formed by a cosine function derived from    said sine function in a manner corresponding to the general equation

${G\left( {x,s} \right)} = {G_{0} + {2*A*{\cos\left( \frac{2*\varphi*x}{L_{REF}} \right)}*{\sin\left( \frac{2*\varphi*\left( {s - c} \right)}{L_{REF}} \right)}} + {2*B*\left( {s - c} \right)}}$where

-   s is the displacement of the upper roll from the central position-   G₀ is the roll gap offset.

By inserting the linear element B*(x+c) into the equation for the barrelcontour, tilting of the sine function is made possible and, by suitablechoice of the coefficient (B), minimizing of the differences in diameteralong the barrel contour is achieved. The minimizing of the differencesin diameter along the effective length of the roll barrel achieved bythe tilted sine function leads at the same time to a reduction in theaxial forces dissipated into the roll supporting bearings during therolling operation. In the case of rolling stands which are equipped withbackup rolls in addition to the work rolls provided with a barrelcontour, the optimization of the tilting coefficient leads to areduction in the maximum local contact pressures on the backup rolls, orgenerally to a more uniform distribution of forces on the neighbouringrolls. The tilting coefficient (B) consequently brings about a smoothingof the contour profile on the roll barrel and of the distribution offorces. Consequently, although the introduction of a tilting coefficientinto the contour equation of the roll barrels favorably influences theloading to which the rolls and bearings of the rolling stand aresubjected, it does not exhibit any fundamental influence on the roll gapgeometry, as shown by the comparison of the two roll gap equations basedon a sine function and a tilted sine function for the roll barrelcontour.

As can be seen from the above formula for G(x,s), the two barrelcontours complement one another when the displacement of the upper workroll corresponds to the contour displacement c and at the same timethere is an equal and opposite displacement of the lower work roll bys=−c. This position may in this case lie both inside and outside theworking range of the axial displacement.

An advantageous configuration of the curved barrel contour is obtainedif, with a given camber reference length (L_(REF)) for the curved barrelcontour of the roll, a contour angle (φ) corresponding to the condition0°<φ≦180°, preferably 50°≦φ≦80°, is chosen. This ensures that, startingfrom the central maximum or minimum value, the roll gap constantlydecreases or increases to the edges of the roll depending on the chosendirection of displacement. In the case of a contour angle φ>180°, thereis a reversal in the constant decrease or increase of the roll gap inthe edge region of the camber reference length, and consequentlyundesired influences on the quality of the roll strip. If the contourangle approaches the value φ=0, there is an asymptomatic trend towardthe formation of a parabolic roll gap contour.

There is an approximation to minimizing the axial forces to bedissipated into the roll supporting bearings when the tiltingcoefficient (B) in the equation for the barrel contour of each roll ischosen such that the maximum difference in diameter of the barrelcontours within the camber reference length or the barrel length is at aminimum.

Influencing the rolls in such a way as to improve the quality of thestrip can be obtained if further actuators, influencing the barrelcontour at least in certain portions, are additionally positioned in therolling stand in operative connection with the work rolls and/or backuprolls and/or intermediate rolls, such as for example work roll coolingor zone cooling. Corresponding effects may also be realized by rollbending devices or by heating devices which can be zonally switched on.

In order to ensure continuous monitoring and influencing of the qualityof the strip, inclusion of the rolling stand in a profile or flatnesscontrol circuit is envisaged. This is achieved by the work rolls and/orbackup rolls and/or intermediate rolls being connected to a controldevice for profile or flatness control by the displacing devicesassigned to them, and also if appropriate necessary measuring devicesfor sensing the state of the strip running in or running out and, ifappropriate, additional actuators, by the control device being assigneda computing unit, which uses mathematical models, if appropriate uses aneural network, to generate control signals for the correction of thework rolls and/or backup rolls and/or intermediate rolls and, ifappropriate, additional actuators, and actuating elements assigned tothe work rolls and/or backup rolls and/or intermediate rolls and ifappropriate additional actuators can be used to move them to positionscorresponding to the control signals. The measuring devices are used toacquire strip-specific data, such as for example profile variation,stress conditions, temperature profiles and rolling forces.

BRIEF DESCRIPTION OF THE DRAWINGS

Further advantages and features of the present invention emerge from thedescription which follows of nonrestrictive exemplary embodiments,reference being made to the accompanying figures, in which:

FIG. 1 shows the schematic representation of a two-high rolling standcorresponding to the invention,

FIG. 1 a schematically shows work rolls

FIG. 1 b illustrates a roll gap contour

FIG. 2 shows a schematic representation of a four-high rolling standwith backup rolls corresponding to the invention,

FIG. 3 shows a schematic representation of a six-high rolling stand withintermediate rolls corresponding to the invention,

FIG. 4 shows the roll barrel contour according to the invention on thebasis of a sine function,

FIG. 4 a shows part of a roll combined with a sine contour

FIG. 5 shows the roll barrel contour according to the invention on thebasis of a tilted sine function,

FIG. 6 shows a geometrical definition of the contour angle,

FIG. 7 shows the idle roll gap contour in dependence on the contourangle,

FIG. 8 shows the roll gap contour in dependence on the roll displacements

FIG. 9 schematically shows a control device for profile and flatnesscontrol.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Various types of rolling stands that are considered for application ofthe invention and which have known basic structure in the prior art, forexample EP-B 0 049 798, to which the invention is here applied areschematically represented in FIGS. 1 to 3.

FIG. 1 shows a two-high rolling stand 1 with stand uprights 2 and a pairof work rolls 3, 4, which are rotatably supported in chocks 5, 6 in thetwo stand uprights 2. Adjusting devices 7 make it possible to adjust thetwo work rolls 3, 4 with respect to the rolled strip 9 running throughthe roll gap 8. The two work rolls 3, 4 are supported in an axiallydisplaceable manner by means of the roll necks 10, 11 in the chocks 5,6, which also comprise displacing devices 12, 13. The roll barrels 14 ofthe two work rolls 3, 4 are provided with a curved barrel contour 15over their entire effective barrel length, these barrel contours 15complementing one another in a specific relative axial position of thework rolls in the unloaded state. This is possible either inside oroutside the axial displacement region of the work rolls 3, 4.

FIG. 1 a schematically shows two work rolls in a working position andFIG. 1 b illustrates the roll gap contour G dependent upon thedisplacements.

FIG. 2 shows in a further schematized representation a four-high rollingstand 17 with work rolls 3, 4 and backup rolls 18, 19. In this exemplaryembodiment, the backup rolls 18, 19 are provided with a curved barrelcontour 15 and are supported in an axially displaceable manner. Byanalogy, FIG. 3 shows a six-high rolling stand 20 with work rolls 3, 4,backup rolls 18, 19 and intermediate rolls 21, 22. In this exemplaryembodiment, the intermediate rolls 21, 22 are provided with a curvedbarrel contour 15 and are supported in an axially displaceable manner.While in the case of the two-high rolling stand the barrel contour actsdirectly on the roll strip, in the case of the rolling stands accordingto FIG. 2 and FIG. 3 a change of the roll gap contour produced by theessentially cylindrical work rolls is brought about by the effect of thebackup or intermediate rolls provided with a curved barrel contour.

In the various embodiments of FIGS. 1-3, either the work rolls may havethe curved barrel contour, or the intermediate rolls, or the backuprolls, or only the outermost rolls in the respective stands of theembodiments, or all rolls in the respective stands of the embodiments.Each roll has the curved barrel contour described below.

All of the rolls, work, intermediate and backup, are of steel and aredeformable under pressure during the rolling process. The rolling forceduring that process is high enough to deform each cylindrical roll to becontoured as described herein. The extent of the roll deformation is inthe range of a few tenths of a millimeter.

The profile of the barrel contour of the rolls of a pair of rolls isformed by a trigonometric function, preferably a sine function,particular advantages being obtained by a barrel contour produced by atilted sine function, these advantages lying in possible minimizing ofthe differences in diameter along the barrel contour. FIG. 4 shows thecurved contour profile on the roll barrel of the upper and lower workrolls of a two-high rolling stand on the basis of a sine function in thecase of a roll barrel length of 1540 mm and a contour angle of 72°. Inthe case of a work roll displacement of approximately ±60 mm, markeddifferences in diameter over the barrel length are already evident.

FIG. 4 a shows a part of a roll combined with a sine contour. It isbased on a coordinate system (R,x), wherein the roll axis complies withthe x-axis of the coordinate system such that the various factors of theequation above are shown.

FIG. 9 shows the control device for the profile and the flatnesscontrol. In order to ensure continuous monitoring and influencing of thequality of the strip 9, inclusion of the rolling stand in a profile orflatness control circuit is envisaged. This is achieved by the workrolls 3, 4 and/or backup rolls 18, 19 and/or intermediate rolls beingconnected to a control device for profile 32 or flatness 33 control bythe displacing devices 12, 13 assigned to them; and also if appropriate,necessary measuring devices for sensing the state of the strip runningin or running out; and, if appropriate, additional actuators 30, 31, bythe control device being assigned a computing unit 34, which usesmathematical models; and if appropriate uses a neural network, togenerate control signals for the correction of the work rolls and/orbackup rolls and/or intermediate rolls; and, if appropriate, additionalactuators, 30, 31 and actuating elements assigned to the work rollsand/or backup rolls and/or intermediate rolls; and if appropriateadditional actuators can be used to move them to positions correspondingto the control signals. The measuring devices are used to acquirestrip-specific data, such as for example profile variation, stressconditions, temperature 36 profiles and rolling forces 37.

By contrast, FIG. 5 shows the curved contour profile on the roll barrelon the basis of a tilted sine function. The differences in diameter overthe roll barrel length are much smaller here and illustrate thesmoothing effect described. Tests have shown that, with roll barrelscontoured in such a way, a rolled strip which meets the highest qualityrequirements, is planar and free from undulations is obtained.

Advantages exist with regard to the clearly evident input variables andthe consequently easier transferability to other stand configurations.Input variables are the camber reference length or the barrel length,the displacement region, the equivalent roll cambers in the extremedisplacement positions and the contour angle.

In FIG. 6, the significance of these variables for a specificstandardized roll gap profile is illustrated by the example of a contourangle of 70°. The contour angle defines that section of the cosine curvethat corresponds to half the camber reference length on the barrel.

The barrel contour can be influenced by variation of the contour angle.The choice of a larger contour angle leads to a smaller diameter of theroll barrel in a region between the center of the roll and the edge ofthe roll, consequently to a smaller local degree of reduction in theroll strip thickness and ultimately a minimization of the formation ofundulations in the quarter area in this region. Influence of the contourangle on the idle roll gap contour is represented in FIG. 7 and clearlyshows the diameter variation in the quarter area.

To allow the rolls provided with the barrel contour described to be usedfor dynamic flatness control, the roll gap contour must be determined bythe displacement position of the rolls and be continuously variable overthe displacement region. These conditions are represented in FIG. 8 forthree values given by way of example for the roll displacement of theupper roll (s) of −60 mm, 0 mm (no displacement) and +60 mm and show theeffective range of the rolling stand that can be used.

1. A rolling stand for producing rolling strip, comprising: a stand forsupporting rolls; two work rolls supported in the stand and oriented todefine a roll gap between which a strip is rolled; each roll of the twowork rolls having a respective effective barrel length and having arespective curved barrel contour extending axially over the entireeffective barrel length of the rolls, wherein the respective barrelcontours complement one another when the rolls are in a specificrelative axial position in an unloaded state; the rolls being supportedin the stand for being axially displaceable with respect to one another;the respective barrel contour of each of the two rolls is formedaccording to a trigonometric function; the roll gap between the tworolls having a contour that is also formed by a trigonometric functionwhich is dependent upon a profile of the barrel contour and upon theaxial position of the rolls within an axial displacement region thereofwherein the trigonometric function of the barrel contour is a tiltedsine function corresponding to the general equation${R(x)} = {R_{0} + {A*{\sin\left( \frac{2*\varphi*\left( {x + c} \right)}{L_{REF}} \right)}} + {B*\left( {x + c} \right)}}$where R is the radius of the roll x is the axial position with respectto the center of the roll (=distance from the center of the roll) R₀ isthe roll radius offset A is the contour coefficient φ is the contourangle c is the contour displacement L_(REF) is the camber referencelength B is the tilting coefficient and the roll gap contour is formedby a cosine function derived from the sine function in a mannercorresponding to the general equation${G\left( {x,s} \right)} = {{{G_{0} \div 2}*A*\cos\;\left( \frac{2*\phi*x}{L_{REF}} \right)*{\sin\left( \frac{2*\phi*\left( {s - c} \right)}{L_{REF}} \right)}} + {2*B*\left( {s - c} \right)}}$where s is the displacement of the upper roll from the central positionG₀ is the roll gap offset.
 2. A rolling stand for producing rolledstrip, comprising: a stand for supporting rolls; two work rollssupported in the stand and oriented to define a roll gap between which astrip is rolled; a pair of second rolls, each second roll being outwardof and in pressing engagement on a respective one of the work rolls forurging the work rolls toward the roll gap for producing the rolledstrip; each second roll having a respective effective barrel length andhaving a respective curved barrel contour running over the entireeffective barrel length of the second roll, wherein the respectivebarrel contours of each of the second rolls complement one another whenthe second rolls are in a specific relative axial position of the secondrolls in an unloaded state; the second rolls pressing on the work rollsfor defining respective curved contours of the work rolls correspondingto the respective curved contours of the second rolls in engagement withthe work rolls; the second rolls defining the work rolls to be so shapedthat the profile of the barrel contour of each of the work rolls isformed according to a trigonometric function, and defining the roll gapbetween the work rolls to have a contour that is also formed by atrigonometric function which is dependent upon the profile of the barrelcontour of the second rolls and upon the axial position of the secondrolls within an axial displacement region thereof wherein thetrigonometric function of the barrel contour is a tilted sine functioncorresponding to the general equation${R(x)} = {R_{0} + {A*{\sin\left( \frac{2*\varphi*\left( {x + c} \right)}{L_{REF}} \right)}} + {B*\left( {x + c} \right)}}$where R is the radius of the roll x is the axial position with respectto the center of the roll (=distance from the center of the roll) R₀ isthe roll radius offset A is the contour coefficient φ is the contourangle c is the contour displacement L_(REF) is the camber referencelength B is the tilting coefficient and the roll gap contour is formedby a cosine function derived from the sine function in a mannercorresponding to the general equation${G\left( {x,s} \right)} = {{{G_{0} \div 2}*A*\cos\;\left( \frac{2*\phi*x}{L_{REF}} \right)*{\sin\left( \frac{2*\phi*\left( {s - c} \right)}{L_{REF}} \right)}} + {2*B*\left( {s - c} \right)}}$where s is the displacement of the upper roll from the central positionG₀ is the roll gap offset.
 3. The rolling stand of claim 2, wherein thesecond rolls comprise backup rolls, and a respective one of the backuprolls is in engagement with each of the work rolls for urging each ofthe work rolls toward the roll gap.
 4. The rolling stand of claim 2,wherein the second rolls comprise intermediate rolls, and a respectiveone of the intermediate rolls is in engagement with each of the workrolls for urging each of the work rolls toward the roll gap; arespective backup roll in engagement with each of the intermediate rollsfor urging the respective intermediate roll toward the respective workroll.
 5. The rolling stand of claim 2, wherein the trigonometricfunction of each roll is defined by a sine function, and the roll gapcontour of the work rolls is defined by a cosine function derived fromthe sine function.
 6. The rolling stand of claim 1, wherein thetrigonometric function of each work roll is defined by a sine function,and the roll gap contour of the work rolls is defined by a cosinefunction derived from the sine function.
 7. The rolling stand of claim2, wherein the barrel contour of the two second rolls is such that thetwo barrel contours complement one another inside the axial displacementregion of the rolls.
 8. The rolling stand of claim 1, wherein the barrelcontour of the two rolls is such that the two barrel contours complementone another inside the axial displacement region of the rolls.
 9. Therolling stand as claimed in claim 2, wherein the barrel contour of thetwo second rolls is such that the two barrel contours complement oneanother outside the axial displacement region of the rolls.
 10. Therolling stand as claimed in claim 1, wherein the barrel contour of thetwo work rolls is such that the two barrel contours complement oneanother outside the axial displacement region of the rolls.
 11. Therolling stand as claimed in claim 1, wherein with a given camberreference length (L_(REF)) for the curved barrel contour of the roll,the contour angle (φ) corresponds to the condition 0°<φ≦180°.
 12. Therolling stand as claimed in claim 1, wherein with a given camberreference length (L_(REF)) for the curved barrel contour of the roll,the contour angle (φ) corresponds to the condition 50°≦φ≦80°.
 13. Therolling stand as claimed in claim 1, wherein the tilting coefficient (B)in the equation for the barrel contour of each roll is selected suchthat the maximum difference in diameter of the barrel contours withinthe camber reference length or the barrel length is at a minimum. 14.The rolling stand as claimed in claim 1, wherein the tilting coefficient(B) in the equation for the barrel contour of each roll is such that themaximum difference in diameter of the barrel contours within the camberreference length or the barrel length is at a minimum.
 15. The rollingstand as claimed in claim 2, wherein the tilting coefficient (B) in theequation for the barrel contour of each roll is such that the maximumdifference in diameter of the barrel contours within the camberreference length or the barrel length is at a minimum.
 16. The rollingstand as claimed in claim 2, further comprising actuators operable toinfluence the barrel contour of the second rolls at least in certainportions, the actuators being positioned at the rolling stand inoperative connection with the second rolls.
 17. The rolling stand asclaimed in claim 16, wherein the actuators comprise work roll cooling orzone cooling.
 18. The rolling stand as claimed in claim. 1, furthercomprising actuators operable to influence the barrel contour at leastin certain portions, the actuators being positioned at the rolling standin operative connection with the two roll.
 19. The rolling stand asclaimed in claim 17, wherein the actuators comprise work roll cooling orzone cooling.
 20. The rolling stand of claim 2, further comprising acontrol device for controlling the profile or flatness of the stripproduced by the work rolls; a displacement device connected with thesecond rolls and operable by the control device for axially displacingthe second rolls with respect to each other.
 21. The rolling stand ofclaim 20, wherein the control device further comprises a measuringdevice for sensing the state of the strip being rolled.
 22. The rollingstand of claim 1, further comprising a control device for controllingthe profile or flatness of the strip produced by the work rolls; adisplacement device connected with the two work rolls and operable bythe control device for axially displacing the work rolls with respect toeach other.
 23. The rolling stand of claim 22, wherein the controldevice further comprises a measuring device for sensing the state of thestrip being rolled.
 24. The rolling stand of claim 20, wherein thecontrol device further comprises a respective computing unit which usesmathematical models or a neural network to generate control signals forcorrection of the positions of the second rolls.
 25. The rolling standof claim 20, wherein the control device further comprises a respectivecomputing unit which uses mathematical models or a neural network togenerate control signals for correction of the positions of the secondrolls.
 26. A rolling stand for producing rolled strip, comprising: astand for supporting rolls; two work rolls supported in the stand andoriented to define a roll gap between which a strip is rolled; a pair ofsecond rolls, each second roll being outward of and in pressingengagement on a respective one of the work rolls for urging the workrolls toward the roll gap for producing the rolled strip; each secondroll having a respective effective barrel length and having a respectivecurved barrel contour running over the entire effective barrel length ofthe second roll, wherein the respective barrel contours of each of thesecond rolls complement one another when the second rolls are in aspecific relative axial position of the second rolls in an unloadedstate; the second rolls pressing on the work rolls for definingrespective curved contours of the work rolls corresponding to therespective curved contours of the second rolls in engagement with thework rolls; the second rolls defining the work rolls to be so shapedthat the profile of the barrel contour of each of the work rolls isformed according to a trigonometric function, and defining the roll gapbetween the work rolls to have a contour that is also formed by atrigonometric function which is dependent upon the profile of the barrelcontour of the work rolls and upon the axial position of the work rollswithin an axial displacement region thereof wherein the trigonometricfunction of the barrel contour is a tilted sine function correspondingto the general equationR(x)=R ₀ +A*sin(2*φ*(x+c)/L _(REF))+B*(x+c) where R is the radius of theroll x is the axial position with respect to the center of the roll(=distance from the center of the roll) R₀ is the roll radius offset Ais the contour coefficient φ is the contour angle c is the contourdisplacement L_(REF) is the camber reference length B is the tiltingcoefficient and the roll gap contour is formed by a cosine functionderived from the sine function in a manner corresponding to the generalequationG(x·s)=G ₀+2*A*cos(2*φ*x/L _(REF)) *sin(2*φ*(s−c)/L _(REF))+2*B*(s−c)where s is the displacement of the upper roll from the central positionG₀ is the roll gap offset.
 27. A rolling stand for producing rollingstrip, comprising: a stand for supporting rolls; two work rollssupported in the stand and oriented to define a roll gap between which astrip is rolled; each work roll of the two work rolls having arespective effective barrel length and having a respective curved barrelcontour extending axially over the entire effective barrel length of thework rolls, wherein the respective barrel contours complement oneanother when the work rolls are in a specific relative axial position inan unloaded state; the work rolls being supported in the stand for beingaxially displaceable with respect to one another; the respective barrelcontour of each of the two work rolls is formed according to atrigonometric function; the roll gap between the two work rolls having acontour that is also formed by a trigonometric function which isdependent upon a profile of the barrel contour and upon the axialposition of the work rolls within an axial displacement region thereof;a pair of second rolls, each second roll being outward of and inpressing engagement on a respective one of the work rolls for urging thework rolls toward the roll gap for producing the rolled strip; thesecond rolls pressing on the work rolls for defining the respectivebarrel curved contours of the work rolls corresponding to respectivecurved contours of the second rolls in engagement with the work rolls;each second roll having a respective effective barrel length and havinga respective curved barrel contour running over the entire effectivebarrel length of the second roll, wherein the respective barrel contourof each of the second rolls complements the contour of the other secondroll and the respective contour of the barrel contour of the respectiveone of the work rolls engaged by each second roll complements therespective second roll when both the work rolls and the second rolls arein specific relative axial positions of the work rolls and the secondrolls in an unloaded state; the second rolls defining the work rolls tobe so shaped that the profile of the barrel contour of each of the workrolls is formed according to a trigonometric function, and defining theroll gap between the work rolls to have a contour that is also formed bya trigonometric function which is dependent upon the profile of thebarrel contour of the second rolls and upon the axial position of thework rolls within an axial displacement region thereof wherein thetrigonometric function of the barrel contour is a tilted sine functioncorresponding to the general equationR(x)=R ₀ +A*sin(2*φ*(x+c)/L _(REF))+B*(x+c) where R is the radius of theroll x is the axial position with respect to the center of the roll(=distance from the center of the roll) R₀ is the roll radius offset Ais the contour coefficient φ is the contour angle c is the contourdisplacement L_(REF) is the camber reference length B is the tiltingcoefficient and the roll gap contour is formed by a cosine functionderived from the sine function in a manner corresponding to the generalequationG(x·s)=G ₀+2*A*(2*φ*x/L _(REF))*sin (2*φ*(s−c)/L _(REF))+2*B*(s−c) wheres is the displacement of the upper roll from the central position G₀ isthe roll gap offset.
 28. A rolling stand for producing rolling strip,comprising: a stand for supporting rolls; two work rolls supported inthe stand and oriented to define a roll gap between which a strip isrolled; each work roll of the two work rolls having a respectiveeffective barrel length and having a respective curved barrel contourextending axially over the entire effective barrel length of the workrolls, wherein the respective barrel contours complement one anotherwhen the work rolls are in a specific relative axial position in anunloaded state; the work rolls being supported in the stand for beingaxially displaceable with respect to one another; the respective barrelcontour of each of the two work rolls is formed according to atrigonometric function; the roll gap between the two work rolls having acontour that is also formed by a trigonometric function which isdependent upon a profile of the barrel contour and upon the axialposition of the work rolls within an axial displacement region thereof;a pair of intermediate rolls, each intermediate roll being outward ofand in pressing engagement on a respective one of the work rolls forurging the work rolls toward the roll gap for producing the rolledstrip; the intermediate rolls pressing on the work rolls for definingthe respective curved barrel contours of the work rolls corresponding torespective curved contours of the intermediate rolls in engagement withthe work rolls; each intermediate roll having a respective effectivebarrel length and having a respective curved barrel contour running overthe entire effective barrel length of the intermediate roll, wherein therespective barrel contour of each of the intermediate rolls complementsthe contour of the other intermediate roll and the respective barrelcontour of the respective one of the work rolls engaged by eachintermediate roll complements the respective contour of the intermediateroll when both the work rolls and the intermediate rolls are in specificrelative axial positions of the work rolls and the intermediate rolls inan unloaded state; the intermediate rolls defining the work rolls to beso shaped that the profile of the barrel contour of each of the workrolls is formed according to a trigonometric function, and defining theroll gap between the work rolls to have a contour that is also formed bya trigonometric function which is dependent upon the profile of thebarrel contour of the intermediate rolls and upon the axial position ofthe work rolls within an axial displacement region thereof; a respectivebackup roll in engagement with each of the intermediate rolls for urgingthe respective intermediate roll toward the respective work roll; eachbackup roll having a respective effective barrel length and having arespective curved barrel contour running over the entire effectivebarrel length of the backup roll, wherein the respective barrel contourof each of the backup rolls complements the contour of the other backuproll and the respective barrel contour of the respective one of theintermediate rolls engaged by each backup roll complements therespective backup roll when all of the work rolls, the intermediaterolls and the backup rolls are in specific relative axial positions ofthe work rolls the intermediate rolls and the backup rolls in anunloaded state; the intermediate rolls and the backup rolls defining thework rolls to be so shaped that the profile of the barrel contour ofeach of the work rolls is formed according to a trigonometric function,and defining the roll gap between the work rolls to have a contour thatis also formed by a trigonometric function which is dependent upon theprofile of the barrel contour of the intermediate rolls and the backuprolls and upon the axial positions of the work rolls, the intermediaterolls and the backup rolls within an axial displacement region thereofwherein the trigonometric function of the barrel contour is a tiltedsine function corresponding to the general equationR(x)=R ₀ +A*sin(2*φ*(x+c)/L _(REF))+B*(x+c) where R is the radius of theroll x is the axial position with respect to the center of the roll(=distance from the center of the roll) R₀ is the roll radius offset Ais the contour coefficient φ is the contour angle c is the contourdisplacement L_(REF) is the camber reference length B is the tiltingcoefficient and the roll gap contour is formed by a cosine functionderived from the sine function in a manner corresponding to the generalequationG(x·s)=G ₀+2*A*cos(2*φ*x/L _(REF)) *sin(2*φ*(s−c)/L _(REF))+2*B*(s−c)where s is the displacement of the upper roll from the central positionG₀ is the roll gap offset.